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Chapter 1: Q51P (page 96)

A toy rocket is launched with an initial velocity of 12.0 m/s in the horizontal direction from the roof of a 30.0m tall building. The rocket鈥檚 engine produces a horizontal acceleration of (160m/s3)t, in the same direction as the initial velocity, but in the vertical direction the acceleration is g, downward. Ignore air resistance. What horizontal distance does the rocket travel before reaching the ground?

Short Answer

Expert verified

The horizontal distance the rocket travel before reaching ground 5087.53m.

Step by step solution

01

Newton’s law

The velocity contains two components, one is horizontal component and another one is vertical.

According to the newton鈥檚 laws of motion,

s=ut+12at2

Where, s, u, t, a, are displacement, initial velocity, time and acceleration.

From the newton鈥檚 law of motion

v=u+at

Here v, u, a, t are final velocity, initial velocity, acceleration due to gravity, and time.

02

Given

Initial velocity = 12.0m/s

Building = 30m

Horizontal Acceleration =160m/s3t

03

Horizontal distance travel by rocket before reaching the ground

For the vertical motion from the law of motion of Newton,

s=ut+12at230m=12m/s脳t+12脳9.8m/s2脳t2t=3.979s

For the horizontal motion,

s=ut+12at2s=12m/s脳3.979s+12脳160m/s3脳3.979s3s=5087.53m

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